I've wondered if some of the "circle" varieties are really spirals rather than concentric circles. Thinking about how the die was made, it would seem simpler to have a lathe set to cut a spiral on the face rather than having to set up 40-50 separate cuts of a circle. Can you tell by looking at the center of the chip?

Maybe you could try one on your old phonograph... who knows there might be some music there [g].